Over at Better Explained, Kalid also has a wonderful intro, with his own animated visualizations.
Fourier transforms form the backbone of X-ray crystallograpy one of the most useful experimental discoveries in science. At the Royal Institution, Prof. Stephen Curry gave a popular lecture — Seeing things in a different light: How X-ray crystallogroaphy revealed the structure of everything — about the method and how its awesome power has been used for determining the atomic level details of molecules with as many as 1000s of atoms. Well worth an hour of your time, since it gives a nice overview of some of the recent developments. If you studied x-ray crystallography as a part of physics, chemistry, or materials science, you might want to skip ahead to the 20 minute mark or so. Here’s the YouTube link, if the embed doesn’t work [Also check out Prof. Curry’s blog post on what went into this talk]:
[Update: This short celebratory video from the Royal Institution commemorating 100 years of x-ray crystallography is pretty good!]
The Caravan has a nice article about quasicrystals by Virat Markandeya who uses the lens of Prof. Paul Steinhardt’s decade-long search for naturally occurring quasicrystalline mineral. In addition to describing the work of Prof. Dan Shechtman and Prof. Paul Steinhardt, the article has good bits on the contributions Prof. Roger Penrose and Prof. Alan Mackay.